Maximizing genetic gain I
Walter R. Fehr and Walter P. Suza
Readings:
- Chapters 6 and 7 [PDF], Principles of Cultivar Development. Vol. 1: Theory and Technique, by Walter R. Fehr (Access the full book)
- Chapter 17. 18 and 19 [PDF], Principles of Cultivar Development. Vol. 1: Theory and Technique, by Walter R. Fehr
Introduction
A successful program of cultivar development is based on the effective utilization of available resources for selection of superior individuals for traits of importance. The amount of available resources, including facilities, time, and money, and the traits of importance in a new cultivar differ for every breeding program. As a result, no two breeding programs are designed the same. This is evident by comparing the breeding strategies used by different persons to develop cultivars of a plant species that are published in the Journal of Plant Registrations and Horticultural Science.
This section is intended to help you understand the variables that need to be considered in designing an effective breeding program for selection of traits that are quantitatively inherited. Our recommended reading for this section from Principles of Cultivar Development chapter 17, contains a formula that can be used to compare the amount of genetic improvement per year from different breeding strategies.
[latex]G_c = h^{2}D[/latex]
Each of the components in the formula can be influenced by the choices breeders make in carrying out their cultivar development programs. Chapters 6, 7, 18, and 19 in Principles of Cultivar Development are important for understanding how each of the components can be manipulated to maximize genetic improvement.
The formula for genetic gain per year in Chapter 17 of Principles of Cultivar Development is based on the variance component method of calculating heritability. The components used in the formula are derived from analyses of variance, examples of which are provided in tables 17-6 and 17-7 of the chapter (pp. 227–228), reproduced below.
| Source | Degrees of Freedom | Mean Squares | Expected Mean Squares* |
|---|---|---|---|
| Total | 719 | 7.68 | |
| Exvironments (E) | 1 | 281.28 | |
| Replications/E (R/E) | 2 | 27.45 | |
| Lines (L) | 59 | 59.33 M1 | [latex]\sigma^{2}_{w} + n \sigma^{2} + nr\sigma^{2}_{ge} + nrt\sigma^{2}_{g}[/latex] |
| E × L | 59 | 4.00 M2 | [latex]\sigma^{2}_{w} + n \sigma^{2} + nr\sigma^{2}_{ge}[/latex] |
| (R/E) × L | 118 | 3.25 M3 | [latex]\sigma^{2}_{w} + n \sigma^{2}[/latex] |
| Plants/plots | 480 | 2.20 M4 | [latex]\sigma^{2}_{w}[/latex] |
*[latex]n[/latex] = plants per plot = 3; [latex]r[/latex] = replications = 2; [latex]t[/latex] = environments = 2.
[latex]\sigma^{2}_{w} = M_{4} = 2.20[/latex]
[latex]\sigma^{2} = (M_{3} - M_{4})/n = [(\sigma^{2}_{w} + n\sigma^{2}) - \sigma^{2}_{w}] = (3.25 - 2.20)/3 = 0/35.[/latex]
[latex]\sigma^{2}_{e} = M_{3}/n = (\sigma^{2}_{w} + n\sigma^{2})/n = 3.25/3 = 1.08[/latex]
[latex]\sigma^{2}_{ge} = (M_{2} - M_{3})/nrt = [(\sigma^{2}_{w} + n\sigma^{2} + nrt^{2}_{ge}) - (\sigma^{2}_{w} + n\sigma^{2})]/nr = (4.00 = 3.25)/6 = 0.125[/latex]
[latex]\sigma^{2}_{g} = (M_{1} - M_{2})/nrt = [(\sigma^{2}_{w} + n\sigma^{2} + nrt^{2}_{ge}) - (\sigma^{2}_{w} + n\sigma^{2} + nr\sigma^{2}_{ge}) + nrt \sigma^{2}_{g}]/nrt = (59.33 = 4.00)/12 = 4.61.[/latex]
[latex]\sigma^{2}_{ph} = M_{1}/nrt = (\sigma^{2}_{w} + n\sigma^{2} + nr\sigma^{2}_{ge} + nrt\sigma^{2}_{g})/nrt = (\sigma^{2}_{w}/nrt) + (\sigma^{2}/rt) + \sigma^{2}_{g} = 59.33/(2 \times 3 \times 2) = 4.94.[/latex]
Source: Frank, 1980
| Source | Degrees of Freedom | Mean Squares | Expected Mean Squares* |
|---|---|---|---|
| Total | 239 | 5.58 | |
| Exvironments (E) | 1 | 50.47 | |
| Replications/E (R/E) | 2 | 7.81 | |
| Lines (L) | 19 | 40.08 M1 | [latex]\sigma^{2}_{w} + n\sigma^{2} + nr\sigma^{2}_{ge} + nrt\sigma^{2}_{g}[/latex] |
| E × L | 19 | 3.53 M2 | [latex]\sigma^{2}_{w} + n\sigma^{2} + nr\sigma^{2}_{ge}[/latex] |
| (R/E) × L | 38 | 2.29 M3 | [latex]\sigma^{2}_{w} + n\sigma^{2}[/latex] |
| Plants/plots | 160 | 2.16 M4 | [latex]\sigma^{2}_{w}[/latex] |
Heritability is a numerical measure of the reliability of selection for a quantitative trait. The primary value of calculating heritabilities is to compare the expected gain from different strategies of selection, as will be done in Applied Learning Activities 1 and 3. In Applied Learning 1, you will compare the relative effectiveness of selection among individual seeds versus among individual plants for oleic acid. In Applied Learning Activity 3, you will compare the expected genetic gain per year for different methods of selection.
Although heritability is a useful tool for comparing breeding strategies, breeders commonly decide on the reliability of selection without calculating a heritability value. The data for Applied Learning Activity 1 will be used to illustrate this point. In that assignment, you are asked to compare the realized heritability of data obtained from individual seeds versus individual plants derived from the seed. The one with the greatest heritability would be considered the most reliable for selection. However, a breeder may choose to practice selection even if the heritability is low in order to discard seeds or plants that have very little chance of being effective.
With the data for Applied Learning Activity 1, the breeder would decide on the oleic content of the F2:3 lines that would be acceptable. Assume that 50% is an acceptable value. The next step would be to look at the oleic acid value of the seed and plant for each of the lines with >50% oleic acid. In this example, the seed with the lowest value for lines with >50% oleic acid was 40.86% and the plant with the lowest value was 42.42%. The breeder may decide that it would be reasonable in the future to discard all seeds and plants with less than a certain percentage of oleic acid so that time and resources would not be spent evaluating individuals that have little promise of being useful.
Applied Learning Activity 1
You have been hired by a company to breed cultivars for increased oleic acid content, which is a quantitative trait. You want to know if it is practical to select for the trait among single F2 seeds or among individual F2 plants. To help you decide, you conduct an experiment that will make it possible to compute realized heritabilities in a single-cross population formed by crossing a mid-oleic parent with about 60% oleic acid to a normal parent with about 25% oleic acid.
The hybrid F1 plants from the population were harvested in bulk, a total of 50 F2 seeds were analyzed for oleic acid content non-destructively, and each analyzed seed was identified and planted the following season. The identified F2 plants were harvested individually and the oleic acid content of each was determined by gas chromatography with a bulk sample of five F3 seed. The progeny of each F2 plant was grown as a F2:3 line in a multiple location trial, and the oleic acid content was determined for each F2:3 line from each location. The oleic acid content for each F2 seed, F2 plant, and F2:3 line are provided. For this assignment, you will need to submit your answers for each of the following 10 parts.
- Mark with a highlighter the five F2 seeds with the highest oleic acid content. Calculate the mean oleic acid content of the selected F2 seeds. Calculate the mean of all the F2 seeds. Subtract the mean of all the F2 seeds from the mean of the five selected seeds. The remainder will be the denominator for calculating the realized heritability for individual seeds. Show your calculation.
- Mark with the same color highlighter as used in step 1 the oleic acid content of the F2:3 lines that trace to the selected F2 seeds. Calculate the mean oleic acid content of the five F2:3 lines you marked with a highlighter and the mean of all the F2:3 lines. Subtract the mean of all the F2:3 lines from the mean of the five F2:3 lines that you had selected as F2 seeds. The remainder will be numerator for calculating the realized heritability for individual seeds. Show your calculation.
- Divide the remainder in step 2 by the remainder in step 1. The quotient is the realized heritability for individual seeds. Show your calculation.
- With a different colored highlighter, mark the five F2 plants with the highest oleic content. Calculate the mean oleic acid content of the selected F2 plants. Calculate the mean of all the F2 plants. Subtract the mean of all the F2 plants from the mean of the five selected plants. The remainder will be the denominator for calculating the realized heritability for individual plants. Show your calculation.
- Mark with the same color highlighter used in step 4 the oleic acid content of the F2:3 lines that trace to the selected F2 plants. Calculate the mean oleic acid content of the five F2:3 lines you marked with a highlighter. You calculated the mean of all the F2:3 lines in step 2. Subtract the mean of all the F2:3 lines from the mean of the five F2:3 lines that you had selected as F2 plants. The remainder will be numerator for calculating the realized heritability for individual plants. Show your calculation.
- Divide the remainder in step 5 by the remainder in step 4. The quotient is the realized heritability for individual plants. Show your calculation.
- Why would expect the heritability to be greater for selection among individual plants than individual seeds?
- What are reasons to explain why the heritabilities were less than 100%?
- What percentage of oleic acid would you be comfortable to use for discarding seeds? Why?
- What percentage of oleic acid would you be comfortable to use for discarding plants? Why?
- Download the data from table 1: Chapter 1_ALA_Data [XLS]
Review the full data table below:
| Entry | F2 seed | F2 plant | F2:3 line |
|---|---|---|---|
| 1 | 43.43 | 37.51 | 46.21 |
| 2 | 50.15 | 31.24 | 45.78 |
| 3 | 37.73 | 31.41 | 29.43 |
| 4 | 32.27 | 31.83 | 30.80 |
| 5 | 44.59 | 35.31 | 37.33 |
| 6 | 53.97 | 58.25 | 51.84 |
| 7 | 42.44 | 30.44 | 30.43 |
| 8 | 52.00 | 67.06 | 49.43 |
| 9 | 50.25 | 59.42 | 54.37 |
| 10 | 46.94 | 55.74 | 41.47 |
| 11 | 48.05 | 38.78 | 37.34 |
| 12 | 42.39 | 36.32 | 26.91 |
| 13 | 50.66 | 35.74 | 38.83 |
| 14 | 46.61 | 42.42 | 50.85 |
| 15 | 58.64 | 55.12 | 50.89 |
| 16 | 65.28 | 62.70 | 49.72 |
| 17 | 58.19 | 48.81 | 37.62 |
| 18 | 57.23 | 47.80 | 51.38 |
| 19 | 34.60 | 54.55 | 42.51 |
| 20 | 41.68 | 43.43 | 53.83 |
| 21 | 26.51 | 33.98 | 33.18 |
| 22 | 41.64 | 61.38 | 52.72 |
| 23 | 27.43 | 35.88 | 41.20 |
| 24 | 32.06 | 41.34 | 32.95 |
| 25 | 50.58 | 59.24 | 49.45 |
| 26 | 27.64 | 35.13 | 31.96 |
| 27 | 27.83 | 33.26 | 36.43 |
| 28 | 32.48 | 43.80 | 39.85 |
| 29 | 31.23 | 36.82 | 38.16 |
| 30 | 40.86 | 48.31 | 50.09 |
| 31 | 33.49 | 26.58 | 36.97 |
| 32 | 33.12 | 32.47 | 43.60 |
| 33 | 32.55 | 37.61 | 40.14 |
| 34 | 66.30 | 45.14 | 49.19 |
| 35 | 50.50 | 48.60 | 50.76 |
| 36 | 37.30 | 42.27 | 49.79 |
| 37 | 26.33 | 30.92 | 41.35 |
| 38 | 31.05 | 27.53 | 34.22 |
| 39 | 34.33 | 39.33 | 43.02 |
| 40 | 29.18 | 24.41 | 29.09 |
| 41 | 62.95 | 49.13 | 53.41 |
| 42 | 55.05 | 38.71 | 41.77 |
| 43 | 44.33 | 27.14 | 31.01 |
| 44 | 53.27 | 27.58 | 26.05 |
| 45 | 51.27 | 48.12 | 40.62 |
| 46 | 46.97 | 39.87 | 33.90 |
| 47 | 54.32 | 38.17 | 35.92 |
| 48 | 53.28 | 44.64 | 52.40 |
| 49 | 36.65 | 58.35 | 38.88 |
| 50 | 43.05 | 43.98 | 45.69 |
References
Fehr, W. R. (ed). 1987. Principles of Cultivar Development. Vol 1. Theory and Technique. McGraw-Hill, Inc., New York.
